Using a new line search method with gradient direction to solve nonlinear systems of equations

Abstract

Abstract The line search techniques together with the Newton method are the best methods to solve nonlinear systems of equations. These methods use the gradient directions because they required low storage. In this paper, we suggest a new line search algorithm with gradient direction to solve the nonlinear systems of equations. The purpose of this algorithm is to reduce the number of iterations and the function evaluations, and it can increase the effectiveness of the approach. The algorithms global convergence is proved. The numerical results indicates the efficiency of the new algorithm and it is promised for solving nonlinear systems of equations.